How to make the matrices look constant throughout?

Question

I'm trying to make the following matrices look constant throughout, that is not change their size. I'm having trouble with the third.

What do you suggest I use instead or maybe alter this?

First, we write this system using matrices.

\[
\left[
\begin{array}{ccc|c}
1 & 2 & 3 & 4\\
7 & 5 & 3 & 1\\
-2 & -3 & -4 & -5\\
\end{array}
\right]
\]

We preform $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} - 7\mathbf{R_{1}}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} + 2\mathbf{R_{1}}$

\[
\left[
\begin{array}{ccc|c}
1 & 2 & 3 & 4\\
0 & -9 & -18 & -27\\
0 & 1 & 2 & 3\\
\end{array}
\right]
\]

Next we $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} \times -\frac{1}{9}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} - \mathbf{R_{2}}$, for final

\[
\left[
\begin{array}{ccc|c}
1 & 2 & 3 & 4\\
0 & 1 & 2 & 3\\
0 & 0 & 0 & 0\\
\end{array}
\right]
\]

Answer 1

The package nicematrix can compute for you the width of the widest entry of all the matrices in a portion of your document and give that width to all the columns.

For that, you have to use the environment {NiceMatrixBlock} with the key auto-columns-width.

You need several compilations.

\documentclass{article}
\usepackage{nicematrix}

\begin{document}

First, we write this system using matrices.

\begin{NiceMatrixBlock}[auto-columns-width]
\[
\begin{bNiceArray}{RRR|R}
1 & 2 & 3 & 4\\
7 & 5 & 3 & 1\\
-2 & -3 & -4 & -5\\
\end{bNiceArray}
\]
We preform $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} - 7\mathbf{R_{1}}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} + 2\mathbf{R_{1}}$
\[
\begin{bNiceArray}{RRR|R}
1 & 2 & 3 & 4\\
0 & -9 & -18 & -27\\
0 & 1 & 2 & 3\\
\end{bNiceArray}
\]
Next we $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} \times -\frac{1}{9}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} - \mathbf{R_{2}}$, for final
\[
\begin{bNiceArray}{RRR|R}
1 & 2 & 3 & 4\\
0 & 1 & 2 & 3\\
0 & 0 & 0 & 0\\
\end{bNiceArray}
\]
\end{NiceMatrixBlock}
\end{document}

Answer 2

nicematrix allows you to set the column width.

\documentclass{article}
\usepackage{nicematrix}


\begin{document}
First, we write this system using matrices.
\[
\begin{bNiceArray}[columns-width = 2em]{RRR|R}
1 & 2 & 3 & 4\\
7 & 5 & 3 & 1\\
-2 & -3 & -4 & -5\\
\end{bNiceArray}
\]
We preform $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} - 7\mathbf{R_{1}}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} + 2\mathbf{R_{1}}$
\[
\begin{bNiceArray}[columns-width = 2em]{RRR|R}
1 & 2 & 3 & 4\\
0 & -9 & -18 & -27\\
0 & 1 & 2 & 3\\
\end{bNiceArray}
\]
Next we $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} \times -\frac{1}{9}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} - \mathbf{R_{2}}$, for final
\[
\begin{bNiceArray}[columns-width = 2em]{RRR|R}
1 & 2 & 3 & 4\\
0 & 1 & 2 & 3\\
0 & 0 & 0 & 0\\
\end{bNiceArray}
\]
\end{document}

You could also measure the widest entry and use its width.

\documentclass{article}
\usepackage{nicematrix}


\begin{document}
\setbox0\hbox{$-27$}%
\edef\mywd{\the\wd0}%
First, we write this system using matrices.
\[
\begin{bNiceArray}[columns-width=\mywd]{RRR|R}
1 & 2 & 3 & 4\\
7 & 5 & 3 & 1\\
-2 & -3 & -4 & -5\\
\end{bNiceArray}
\]
We preform $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} - 7\mathbf{R_{1}}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} + 2\mathbf{R_{1}}$
\[
\begin{bNiceArray}[columns-width=\mywd]{RRR|R}
1 & 2 & 3 & 4\\
0 & -9 & -18 & -27\\
0 & 1 & 2 & 3\\
\end{bNiceArray}
\]
Next we $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} \times -\frac{1}{9}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} - \mathbf{R_{2}}$, for final
\[
\begin{bNiceArray}[columns-width=\mywd]{RRR|R}
1 & 2 & 3 & 4\\
0 & 1 & 2 & 3\\
0 & 0 & 0 & 0\\
\end{bNiceArray}
\]
\end{document}

Answer 3

Below I define gaussmat as a matrix-like construction/environment that sets a 3 x 3 Gaussian elimination matrix. The column entries are all the same, capturing its argument and passing it on to a measurement scheme from eqparbox. This finds the widest length of the column entries, thereby creating a uniform look across all columns. An optional argument to gaussmat allows you to reset the measurement using a different label, if need be.

\documentclass{article}

\usepackage{mleftright,eqparbox,collcell}

\newcolumntype{R}{>{\collectcell\matcell}r<{\endcollectcell}}
\newcommand{\matcell}[1]{\eqmakebox[\matcelllabel][r]{$#1$}}

\newenvironment{gaussmat}[1][cw]{%
  \def\matcelllabel{#1}%
  \mleft[\begin{array}{ R R R | R }
}{%  
  \end{array}\mright]
}

\begin{document}

First, we write this system using matrices:
\[
  \begin{gaussmat}
     1 &  2 &  3 &  4 \\
     7 &  5 &  3 &  1 \\
    -2 & -3 & -4 & -5 \\
  \end{gaussmat}
\]
We preform $\mathbf{R_2} \rightarrow \mathbf{R_2} - 7\mathbf{R_1}$ and $\mathbf{R_3} \rightarrow \mathbf{R_3} + 2\mathbf{R_1}$:
\[
  \begin{gaussmat}
    1 &  2 &   3 &   4 \\
    0 & -9 & -18 & -27 \\
    0 &  1 &   2 &   3 \\
  \end{gaussmat}
\]
Next we $\mathbf{R_2} \rightarrow \mathbf{R_2} \times -\frac{1}{9}$ and $\mathbf{R_3} \rightarrow \mathbf{R_3} - \mathbf{R_2}$:
\[
  \begin{gaussmat}
    1 & 2 & 3 & 4 \\
    0 & 1 & 2 & 3 \\
    0 & 0 & 0 & 0 \\
  \end{gaussmat}
\]

\end{document}

You need to compile at least twice with every change in the widest element within your gaussmat.